ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 68,   2   (1999)
pp.   345-353

ON SOME GENERALIZATIONS OF $LC$-SPACES
J. DONTCHEV, M. GANSTER and A. KANIBIR

Abstract.  The aim of this paper is to extend the notion of $LC$-spaces, i.e. spaces whose Lindelof subsets are closed. We will consider four weaker forms of this concept and investigate their relationships with $LC$-spaces as well as among themselves. Accordingly, we continue the study of $LC$-spaces and related spaces.

AMS subject classification.  54A05, 54D20, 54G10, 54D25, 54G99
Keywords.  $LC$-space, Lindelof, $P$-space, $F_\sigma$-set, locally Lindelof, $L_1$, $L_2$, $L_3$, $L_4$-space